In the given AR(1)model,y_t = α + ρy_{t - 1},t = 1,2…… ,the Dickey-Fuller distribution refers to the:

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The Dickey-Fuller distribution refers to the asymptotic distribution of the t statistic under the hypothesis ρ - 1 = 0. This test is used to determine whether a time series has a unit root, which indicates non-stationarity. The null hypothesis of the test is that there is a unit root (i.e. ρ - 1 = 0), and the test statistic follows a Dickey-Fuller distribution under this null hypothesis. The critical values of the test can be obtained from tables or software, and the test can be used to determine whether to reject the null hypothesis of a unit root and conclude that the time series is stationary.

In the Given AR(1)model,yt = α + ρYt - 1,t

In the Given AR(1)model,y_t = α + ρY_{t - 1},t